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Quasi-duo and weakly duo skew PBW extensions

In this paper we study the quasi-duo and weakly duo properties for skew PBW extensions. We show that if [Formula: see text] is a right quasi-duo skew PBW extension over a ring [Formula: see text], then [Formula: see text] is right quasi-duo, and that for a right quasi-duo graded skew PBW extension [Formula: see text] over [Formula: see text], the zero-degree homogeneous component of [Formula: see text] is left quasi-duo if and only if [Formula: see text] is left quasi-duo. Moreover, we give a characterization of right quasi-duo rings for a particular kind of bijective quasi-commutative skew PBW extensions. We also show some properties of weakly left or right duo skew PBW extensions.

World Scientific Pub Co Pte Ltd

Héctor Suárez Yésica Suárez José A. Vélez-Marulanda

Journal of Algebra and Its Applications

2026

Title: Quasi-duo and weakly duo skew PBW extensions

Description:

In this paper we study the quasi-duo and weakly duo properties for skew PBW extensions.

We show that if [Formula: see text] is a right quasi-duo skew PBW extension over a ring [Formula: see text], then [Formula: see text] is right quasi-duo, and that for a right quasi-duo graded skew PBW extension [Formula: see text] over [Formula: see text], the zero-degree homogeneous component of [Formula: see text] is left quasi-duo if and only if [Formula: see text] is left quasi-duo.

Moreover, we give a characterization of right quasi-duo rings for a particular kind of bijective quasi-commutative skew PBW extensions.

We also show some properties of weakly left or right duo skew PBW extensions.

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